Coarse-graining atomic displacements in a solid produces both local affine strains and non-affine fluctuations. Here we study the equilibrium dynamics of these coarse grained quantities to obtain space-time dependent correlation functions. We show ho
w a subset of these thermally excited, non-affine fluctuations act as precursors for the nucleation of lattice defects and suggest how defect probabilities may be altered by an {it experimentally realisable} external field conjugate to the global non-affinity parameter. Our results are amenable to verification in experiments on colloidal crystals using commonly available holographic laser tweezer and video microscopy techniques, and may lead to simple ways of controlling the defect density of a colloidal solid.
We describe the microstructure, shape and dynamics of growth of a droplet of martensite nucleating in a parent austenite during a solid-solid transformation, using a Landau theory written in terms of conventional affine, elastic deformations and {em
non-affine} degrees of freedom. Non-affineness, $phi$, serves as a source of strain incompatibility and screens long-ranged elastic interactions. It is produced wherever the local stress exceeds a threshold and anneals diffusively thereafter. A description in terms of $phi$ is inevitable when the separation between defect pairs, possibly generated during the course of the transformation, is small. Using a variational calculation, we find three types of stable solutions ({hv I}, {hv II} and {hv III}) for the structure of the product droplet depending on the scaled mobilities of $phi$ parallel and perpendicular to the parent-product interface and the stress threshold. In {hv I}, $phi$ is vanishingly small, {hv II} involves large $phi$ localized in regions of high stress within the parent-product interface and {hv III} where $phi$ completely wets the parent-product interface. While width $l$ and size $W$ of the twins follows $lproptosqrt{W}$ in solution {hv I}, this relation does not hold for {hv II} or {hv III}. We obtain a dynamical phase diagram featuring these solutions and argue that they represent specific microstructures such as twinned or dislocated martensites.
Nucleation of a solid in solid is initiated by the appearance of distinct dynamical heterogeneities, consisting of `active particles whose trajectories show an abrupt transition from ballistic to diffusive, coincident with the discontinuous transitio
n in microstructure from a {it twinned martensite} to {it ferrite}. The active particles exhibit intermittent jamming and flow. The nature of active particle trajectories decides the fate of the transforming solid -- on suppressing single particle diffusion, the transformation proceeds via rare string-like correlated excitations, giving rise to twinned martensitic nuclei. These string-like excitations flow along ridges in the potential energy topography set up by inactive particles. We characterize this transition using a thermodynamics in the space of trajectories in terms of a dynamical action for the active particles confined by the inactive particles. Our study brings together the physics of glass, jamming, plasticity and solid nucleation.
Confining a colloidal crystal within a long narrow channel produced by two parallel walls can be used to impose a meso-scale superstructure of a predominantly mechanical elastic character [Chui et al., EPL 2008, 83, 58004]. When the crystal is compre
ssed in the direction perpendicular to the walls, we obtain a structural transition when the number of rows of particles parallel to the walls decreases by one. All the particles of this vanishing row are distributed throughout the crystal. If the confining walls are structured (say with a corrugation along the length of the walls), then these extra particles are distributed neither uniformly nor randomly; rather, defect structures are created along the boundaries resembling soliton staircases, inducing a non-uniform strain pattern within the crystal. Here we study the conditions of stability, formation and annihilation of these solitons using a coarse grained description of the dynamics. The processes are shown by comparing superimposed configurations as well as molecular animations obtained from our simulations. Also the corresponding normal and shear stresses during the transformation are calculated. A study of these dynamical processes should be useful for controlling strain wave superstructures in the self-assembly of various nano- and meso scaled particles.
